Skip to main content
SpringerLink
Log in

On the new soliton and optical wave structures to some nonlinear evolution equations

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

In this study, with the aid of the Wolfram Mathematica software, the powerful sine-Gordon expansion method is utilized to search for the solutions to some important nonlinear mathematical models arising in nonlinear sciences, namely, the (2 + 1) -dimensional Zakharov-Kuznetsov modified equal width equation, the cubic Boussinesq equation and the modified regularized long wave equation. We successfully obtain some new soliton, singular soliton, singular periodic waves and kink-type solutions with complex hyperbolic structures to these equations. We also present the two- and three-dimensional shapes of all the solutions obtained in this study. We further give the physical meaning of all the obtained solutions. We compare our results with the existing results in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M.A. Abdelkawy, M.A. Alghamdi, A.H. Bhrawy, Sci. Res. Essays 7, 2417 (2012)

    Article  Google Scholar 

  2. W.X. Ma, B. Fuchssteiner, Int. J. Non-linear Mech. 31, 329 (1996)

    Article  Google Scholar 

  3. H.M. Baskonus, M. Askin, Travelling wave simulations to the modified Zakharov-Kuzentsov model arising in plasma physics, in 6th International Youth Science Forum “Litteris et Artibus” Computer Science and Engineering, Lviv, Ukraine, 24-26 November, 2016 (Lviv, Polytechnic Publishing House, 2016)

  4. N. Rahma, Md. Nur Alam, H. Or-Roshid, S. Akter, M.A. Akbar, Afr. J. Math. Comput. Sci. Res. 7, 1 (2014)

    Article  Google Scholar 

  5. W.X. Ma, J.H. Lee, Chaos, Solitons Fractals 42, 1356 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  6. E.M.E. Zayed, S.A.H. Ibrahim, Afr. Chin. Phys. Lett. 29, 060201 (2012)

    Article  Google Scholar 

  7. W.X. Ma, T. Huang, Y. Zhang, Phys. Scr. 82, 065003 (2010)

    Article  ADS  Google Scholar 

  8. W.X. Ma, Z. Zhu, Appl. Math. Comput. 218, 11871 (2012)

    Article  MathSciNet  Google Scholar 

  9. W.X. Ma, E. Fan, Comput. Math. Appl. 61, 950 (2011)

    Article  MathSciNet  Google Scholar 

  10. W.X. Ma, Stud. Nonlinear Sci. 2, 140 (2011)

    Google Scholar 

  11. W.X. Ma, Y. Liu, Commun. Nonlinear Sci. Numer. Simul. 17, 3795 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  12. W.X. Ma, Sci. Chin. Math. 55, 1769 (2012)

    Article  Google Scholar 

  13. H. Bulut, H.M. Baskonus, E. Cuvelek, Math. Lett. 1, 10 (2015)

    Google Scholar 

  14. H. Bulut, Abstr. Appl. Anal. 2013, 742643 (2013)

    Google Scholar 

  15. H.M. Baskonus, H. Bulut, Waves Random Complex Media 25, 576 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  16. H.M. Baskonus, D. Altan-Koc, H. Bulut, Nonlinear Sci. Lett. A 7, 67 (2016)

    Google Scholar 

  17. M.F. Aghdaei, J. Manafianheris, J. Appl. Math. Phys. 3, 1571 (2015)

    Article  Google Scholar 

  18. H. Naher, F. Abdullah, World Appl. Sci. J. 16, 1559 (2012)

    Google Scholar 

  19. A.M. Wazwaz, J. Math. Phys. 16, 1212 (1977)

    Google Scholar 

  20. Md. Nur Alam, M.A. Akbar, J. Assoc. Arab Univ. Basic Appl. Sci. 17, 6 (2015)

    Google Scholar 

  21. H.M. Baskonus, AIP Conf. Proc. 1798, 020018 (2017)

    Article  Google Scholar 

  22. A. Yokus, H.M. Baskonus, T.A. Sulaiman, H. Bulut, Numer. Methods Partial Differ. Equ., Numerical simulation and solutions of the two-component second order KdV evolutionary system, https://doi.org/10.1002/num.22192 (2017)

  23. Y. Xu, K. Sun, S. He, L. Zhang, Eur. Phys. J. Plus 131, 186 (2016)

    Article  Google Scholar 

  24. L. Zhang, K. Sun, S. He, H. Wang, Y. Xu, Eur. Phys. J. Plus 132, 31 (2017)

    Article  ADS  Google Scholar 

  25. C. Yan, Phys. Lett. A 22, 77 (1996)

    Article  ADS  Google Scholar 

  26. H. Bulut, T.A. Sulaiman, H.M. Baskonus, A.A. Sandulyak, Optik 135, 327 (2017)

    Article  ADS  Google Scholar 

  27. H.M. Baskonus, H. Bulut, T.A. Sulaiman, Indian J. Phys. 135, 327 (2017)

    Google Scholar 

  28. H. Bulut, T.A. Sulaiman, H.M. Baskonus, F. Erdogan, Eur. Phys. J. Plus 132, 350 (2017)

    Article  Google Scholar 

  29. C.M. Khalique, K.R. Adem, Math. Comput. Model. 54, 184 (2011)

    Article  Google Scholar 

  30. A.J.M. Jawad, M.D. Petkovic, A. Biswas, Sci. Iran. B 20, 179 (2013)

    Google Scholar 

  31. R. Arora, A. Kumar, Appl. Math. 1, 59 (2011)

    Article  Google Scholar 

  32. D.M. Mothibi, C.M. Khalique, Symmetry 7, 949 (2015)

    Article  MathSciNet  Google Scholar 

  33. S. Munro, E.J. Parkes, J. Plasma Phys. 62, 305 (1999)

    Article  ADS  Google Scholar 

  34. D.H. Peregrine, J. Fluid. Mech. 25, 321 (1966)

    Article  ADS  Google Scholar 

  35. A.K. Khalifa, K.R. Raslan, H.M. Alzubaidi, Appl. Math. Model. 32, 2962 (2008)

    Article  MathSciNet  Google Scholar 

  36. Z. Yan, H. Zhang, Phys. Lett. A 252, 291 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  37. H.M. Baskonus, Nonlinear Dyn. 86, 177 (2016)

    Article  MathSciNet  Google Scholar 

  38. E.W. Weisstein, Concise Encyclopedia of Mathematics, 2nd edition (CRC Press, New York, 2002)

Download references

Author information

Authors and Affiliations

  1. Firat University, Department of Mathematics, Elazig, Turkey

    Hasan Bulut & Tukur Abdulkadir Sulaiman

  2. Department of Mathematics, Federal University, Jigawa, Nigeria

    Tukur Abdulkadir Sulaiman

  3. Department of Computer Engineering, Munzur University, Tunceli, Turkey

    Haci Mehmet Baskonus

Authors
  1. Hasan Bulut
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tukur Abdulkadir Sulaiman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haci Mehmet Baskonus
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hasan Bulut.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bulut, H., Sulaiman, T.A. & Baskonus, H.M. On the new soliton and optical wave structures to some nonlinear evolution equations. Eur. Phys. J. Plus 132, 459 (2017). https://doi.org/10.1140/epjp/i2017-11738-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2017-11738-7

Search

Navigation